I've had two issues - one inbound and the other outbound. I was living in the UK at the time.
1st one, my shotgun made it to JHB and cleared customs etc but when I checked it for the flight to Durban it went to Nelspruit or Phalaborwa. I actually saw the dumbass baggage handler (who walked through the boarding gate and onto the apron with me) load it onto the plane next door - I was sitting in my window seat watching this unfold but unable to do a damn thing about it. Needless, to say it was fun & games in Durban because technically and legally I had to have the gun in my possession at all times under the terms of the temp import permit and the SA Police official was very excited to remind of this. So by leaving Durban airport without the shotgun, I was breaking the law. SAA could have given less of a $h!t about helping me - long story short, I got a call 3 or 4 days later saying I could come and collect it at the airport. No assistance in getting it to me or compensating me for the 5 hr round trip to collect it. At least I had some time before the hunt commenced, so I was not inconvenienced from a hunting perspective.
2nd time I was returning from SA to the UK with KLM via Amsterdam (another fun story was getting the firearms permit to transit through Amsterdam) and my gun was nowhere to be found on arrival at Heathrow. An hour or so of paperwork and I was on my way without the gun but with their airline's undertaking to deliver it to my house. Which they duly did but the case was severely damaged, as was the stock in multiple places. Some credit to KLM, they paid me out in full for my claim when the likelihood was that a friendly baggage handler somewhere was responsible. But at the end of the day my gun was damaged en route...